Valérie Trierweiler, the partner of the French president, François Hollande, has been taken to hospital with "exhaustion" following claims that he has been having an affair, it has emerged.

After hearing of Hollande's alleged trysts with the actor Julie Gayet, Trierweiler, a journalist, was taken to hospital where doctors prescribed rest. Trierweiler's office told L'Express magazine she had been taken to hospital on Friday afternoon and was due to be released on Monday.

An unidentified Élysée official told Le Monde that Trierweiler was suffering a "severe case of the blues".

The news came as Hollande's former partner and the mother of his children, Ségolène Royal, told a French news channel on Sunday that France should "turn the page" on their president's alleged affair with Gayet.

Her sentiment was echoed by a poll, published in the Journal du Dimanche, which found 77% of French respondents believed the affair was a personal matter, while 84% said their opinion of Hollande was unchanged by the revelations.

The survey is the first carried out after the celebrity magazine Closer alleged the president had been meeting Gayet in a borrowed flat near the Elysée palace.

The magazine showed photographs of a man in a black helmet, alleged to be Hollande, being accompanied to and from the apartment by a bodyguard on a scooter on 30 and 31 December.

Hollande, 59, who is accompanied on official engagements by Trierweiler, reacted to the magazine's claims in a personal capacity with a threat to sue Closer on the grounds that it had invaded his privacy.

The article was removed from Closer's website following what the magazine described as a "very clear" legal injunction from Gayet's lawyers. Hollande has not denied the affair.

Amid whispers of an affair, the French media's rumour mill has reported the presidential couple have been living apart for months, with Hollande no longer staying at Trierweiler's apartment in the 15th arrondissement.

The status of the "first girlfriend", as she is known, has also been the target of criticism by conservative opposition politicians.

One, Daniel Fasquelle of the UMP, asked in a statement: "Is it normal that she remains at the Élysée at taxpayers' expense when the president has other relationships? Who is the First Lady of France today?"

The French public has been equally hostile. A poll on the website of the magazine Le Point showed a majority of readers want Trierweiler to go. Asked on Saturday whether Hollande should announce their separation, 89.2% of the 13,136 people who voted said 'yes', and 10.8% said 'no'.

Royal – Hollande's partner of 23 years and mother of his four children whom he left for Trierweiler - was drawn into scandal on Sunday during an appearance on France2's news programme.

"I don't want to feed the saga with a little sentence which is very, very far from French people's concerns," she said. When the presenter asked whether the issue was "not political", Royal said: "We should turn the page and get back to work."

It was not clear whether she was referring to Hollande, to herself and the president, to Trierweiler, or to the French public as a whole.

Stéphane Le Foll, France's minister of agriculture and a close confidant of the president, said he would not comment on the reported affair before or during a long-scheduled news conference on Tuesday.

The purpose of the press conference is to talk about France, he told RTL radio. Hollande would speak about "growth, unemployment and investment".

The Gayet scandal has come at an unfortunate time for Hollande, who hopes to rebuild confidence in the government's handling of the economy.

In a new year message, the socialist leader made overtures to French bosses – raising eyebrows among the leftist elements of his party – and is expected to flesh out details of a "responsibility pact" with employers who have complained that high taxation is hampering their hiring ability.

According to a poll published in Le Parisien on 4 January, only 31% of French people find him "competent", although 56% say he is "likeable".

Trierweiler has said she found it difficult to adjust to her role as "first girlfriend". It remains to be seen whether the president will respond to French media pressure to "clarify" his relationship with Trierweiler in the coming days.

Friends of Trierweiler have accused the interior minister, Manuel Valls – who is believed to nurture presidential ambitions – of "betrayal".

The news magazine Le Point suggested on its website that Valls must have known of Hollande's movements, and reported that the apartment where he allegedly met Gayet belonged to someone with connections to a criminal gang.

Gayet, who recently played the role of a seductress in the satirical political film Quai d'Orsay, is a 41-year-old Socialist party activist who expressed gushing support for the "humble" and "wonderful" Hollande before the 2012 election.

Anne Hidalgo, the party's candidate to succeed Bertrand Delanoe as Paris mayor, has listed Gayet as one of her support committee members – a list revealed by Le Parisien on Sunday.

Meanwhile, the Journal du Dimanche reported that one of Hollande's first questions to aides following his election was: "How do I get out without being seen?"